Mutational inactivation of the chromatin remodelling protein ATRX is a recurrent molecular alteration in several cancers such as glioblastoma (GBM), which are unresponsive to current treatment regimens. In this project, I sought to develop an effective therapeutic strategy for treating cancers that have ATRX mutations. To begin with, I screened for a potential selective killing compound that targets ATRX deficiency. Initially, I explored the possibility that ATRX mediates the DNA repair pathways that are committed to repair single-stranded DNA (ssDNA) lesions, in which case such ssDNA lesions would be particularly toxic to ATRX-deficient cells. I examined multiple clinical agents whose repair depends on either the base excision repair (BER) or the nucleotide excision repair (NER) pathway, which include topotecan and cisplatin. In parallel, an RNAi screening based on C. elegans fertility was separately conducted to identify the genetic disruptions that specifically targets the xnp-1/ATRX-mutant worms. Each identified RNAi hit was matched to a small molecule inhibitor, which was then examined in human cancer cell lines for selective killing effect. However, none of the tested compounds led to the selective killing of ATRX deficiency in a cell line-independent manner. Further, as the main theme of this project, I investigated the synthetic lethality of ATRX deficiency with the inhibition of WEE1 kinase, a cell cycle regulator. I tested a novel WEE1 inhibitor DB-0123, which can cross the blood-brain barrier, to validate the selective killing effect of an ATRX CRISPR deleted GBM cell line coupled to the isogenic parental cell line. Moreover, I explored the underlying mechanisms of the selective killing, and found that ATRX-deficient cells accumulate stalled replication forks in response to nucleotide shortage that is incurred upon WEE1 inhibition. This leads to DNA damage, DNA double-strand breaks, and to genome instability through the action of the MRE11 exonuclease, which I propose drives excessive nucleolytic degradation of the stalled forks. Subsequent studies revealed that susceptibility to WEE1 inhibition could be induced by hydroxyurea (HU) treatment, small molecule inhibition of PARP1, or G-quadruplex induction, through a functionally analogous mechanism to ATRX deficiency. Strikingly, the concomitant addition of HU at a low dose enhanced the killing selectivity of WEE1 inhibition towards ATRX deficiency, through amplification of replication fork stalling and premature mitotic entry of S phase cells. It is anticipated that this comprehensive approach into analysing the potential cell susceptibility features that can arise from the loss of ATRX function will provide a basis for future studies into the biological functions of ATRX. Moreover, the findings presented here support the small molecule inhibition of WEE1 as a potentially effective therapeutic approach for treating brain and other cancers with ATRX mutations. This study proposes an evidence-based mechanistic model for the WEE1-ATRX selective killing and offers important biochemical indications for devising WEE1 inhibition-based combination therapies against ATRX-mutant cancers.